How to Calculate Sales Tax without a Calculator | Calculating Sales Tax by Hand | Math with Mr. J

Summary

In the video 'Math with Mr. J,' the host teaches viewers how to manually calculate sales tax and the total cost of a purchase. The example uses a price of $59.49 with a 7.5% sales tax. The process involves converting the percentage to a decimal, multiplying it by the price, and then adding the tax to the original price to find the total cost. The host demonstrates each step in detail, including rounding the sales tax to the nearest cent, resulting in a total cost of $63.95.

Takeaways

• 🧮 To calculate sales tax by hand, you first need to convert the sales tax rate from a percentage to a decimal.
• 🔢 The conversion from percentage to decimal is done by dividing by 100 and moving the decimal point two places to the left.
• ✅ The decimal form of a 7.5% sales tax rate is 0.075.
• 🛒 To find out how much sales tax you owe on an item, multiply the item's price by the tax rate in decimal form.
• 📝 When multiplying a decimal by a whole number, you can ignore the decimal for the multiplication and then place it in the correct position in your final answer.
• 📑 The number of digits to the right of the decimal in your final answer should match the number of digits to the right of the decimal in the original price.
• 💵 When dealing with money, it's important to round your sales tax calculation to the nearest hundredth (two decimal places).
• 🔄 If the hundredths place is 5 or more, round up; if it's less than 5, round down.
• 💲 To find the total cost of an item including sales tax, add the calculated sales tax to the original price of the item.
• 📈 When adding decimals, align the decimal points and proceed with the addition as you would with whole numbers.

Q & A

What is the main topic of the video?

The main topic of the video is how to calculate sales tax by hand without using a calculator.

What is the example sales price used in the video?

The example sales price used in the video is $59.49.

What is the sales tax rate used in the example?

The sales tax rate used in the example is 7.5 percent.

How does the video demonstrate converting a percentage to a decimal?

The video demonstrates converting a percentage to a decimal by dividing the percentage by 100 and moving the decimal point two places to the left.

What is the decimal equivalent of the 7.5 percent sales tax rate as shown in the video?

The decimal equivalent of the 7.5 percent sales tax rate is 0.075.

How does the video approach multiplying the sales price by the tax rate?

The video multiplies the sales price by the tax rate in decimal form, taking care to place the decimal in the correct position in the final answer.

What is the result of multiplying $59.49 by the tax rate of 0.075 as shown in the video?

The result of multiplying $59.49 by the tax rate of 0.075 is $4.46, which is the sales tax amount.

How does the video ensure the correct placement of the decimal in the sales tax calculation?

The video ensures the correct placement of the decimal by counting the number of digits to the right of the decimal in the original price and matching that in the final sales tax amount.

What rounding rule is applied to the sales tax calculation in the video?

The video applies the standard rounding rule where if the digit to the right of the last desired decimal place is 5 or more, the last digit is increased by one.

How does the video calculate the total cost including sales tax?

The video calculates the total cost by adding the original price to the calculated sales tax amount, ensuring the decimals are aligned during the addition.

What is the final price including sales tax as presented in the video?

The final price including sales tax is $63.95.

Outlines

00:00

🧮 Calculating Sales Tax by Hand

This paragraph introduces a tutorial on calculating sales tax manually. The presenter, Mr. J, demonstrates how to determine the sales tax on an item priced at $59.49 with a 7.5% tax rate. The process begins by converting the percentage to a decimal by dividing by 100, which transforms 7.5% into 0.075. The next step involves multiplying the item's price by the decimal tax rate to ascertain the sales tax amount. The presenter meticulously shows the multiplication process, emphasizing the importance of aligning the decimal points and carrying over when necessary. The result is then rounded to the nearest hundredth to reflect the typical money format, leading to a sales tax of $4.46.

05:02

💵 Finding the Total Cost with Sales Tax

The second paragraph continues the tutorial by showing how to calculate the total cost of an item inclusive of sales tax. With the sales tax amount determined in the previous step ($4.46), the presenter instructs viewers to add this to the original price of the item ($59.49). The addition is carefully carried out, ensuring the decimal points are aligned. The final total cost is calculated to be $63.95, which includes the original price plus the sales tax. The paragraph concludes with a recap of the entire process, highlighting the importance of manual calculations for understanding sales tax implications, and ends with a sign-off from the presenter.

Keywords

💡Sales Tax

Sales tax is a tax imposed on the sale of goods and services. It is calculated as a percentage of the price and is included in the final cost paid by the consumer. In the video, the concept is central as the host demonstrates how to calculate sales tax by hand on a purchase of $59.49 with a sales tax rate of 7.5 percent. The example illustrates the process of converting the tax rate from a percentage to a decimal and then multiplying it by the price to find the tax amount.

💡Decimal Form

Decimal form is a way of expressing numbers using a base-10 system, where the position of a digit indicates its value relative to a power of 10. In the context of the video, the host converts the sales tax rate from a percentage (7.5%) to a decimal (0.075) by moving the decimal point two places to the left. This conversion is necessary for the multiplication step in calculating the sales tax amount.

💡Percent

A percent is a way to express a number as a fraction of 100. It is used to describe a rate or a proportion. In the video, the sales tax rate is given as a percent (7.5%), which the host then converts to a decimal for calculation purposes. The script explains that 'percent means per 100,' highlighting the step of dividing by 100 to convert to a decimal.

💡Multiplication

Multiplication is a mathematical operation where one number is used to count the number of times another number is added together. In the video, the host uses multiplication to calculate the sales tax by multiplying the price of the item ($59.49) by the tax rate in decimal form (0.075). The multiplication process is explained step by step, emphasizing the placement of the decimal in the final answer.

💡Decimal Places

Decimal places refer to the digits to the right of the decimal point in a number. They indicate the level of precision or the place value of the number. The video script mentions counting the number of digits to the right of the decimal in the original price to determine where to place the decimal in the calculated sales tax. This ensures the tax amount is correctly aligned with the currency's smallest unit.

💡Hundredths Place

The hundredths place is the second position to the right of the decimal point in a number, representing two-hundredths (1/100) of a whole. In the context of the video, the host rounds the calculated sales tax to the hundredths place to reflect the smallest currency unit (cents). This step is important when dealing with money to ensure the final amount is expressed in the correct denomination.

💡Rounding

Rounding is the process of approximating a number to a certain level of precision. In the video, the host rounds the sales tax amount to the nearest cent, which is the hundredths place. This is done by looking at the digit to the right of the hundredths place and applying the standard rounding rules (if the digit is 5 or more, round up; if it's less than 5, round down).

💡Total Cost

Total cost refers to the overall amount to be paid for a purchase, including the original price and any additional fees such as sales tax. The video script demonstrates how to calculate the total cost by adding the original price of the item to the calculated sales tax. The final step of the calculation is to ensure the consumer knows the full amount they will need to pay.

💡Calculator

A calculator is a device used to perform mathematical calculations. The video's introduction mentions that the purpose of the video is to show how to calculate sales tax by hand, without using a calculator. This emphasizes the educational aspect of the video, teaching viewers how to perform the calculation manually, which can be useful in situations where a calculator is not available.

💡Hand Calculation

Hand calculation refers to performing mathematical operations manually, without the aid of a calculator or computer. The video's theme revolves around hand calculation, as the host guides viewers through each step of calculating sales tax manually. This skill is valuable for understanding the underlying math and for situations where technology might not be accessible.

Highlights

Introduction to calculating sales tax by hand without a calculator

Example given: calculating sales tax on $59.49 with a 7.5% tax rate

Conversion of sales tax rate from percentage to decimal form

Moving the decimal point twice to the left to convert 7.5% to 0.075

Multiplication of the original price by the tax rate in decimal form

Detailed step-by-step multiplication of 59.49 by 0.075

Explanation of placing the decimal in the multiplication result

Final multiplication result and placement of the decimal point

Rounding the sales tax to the nearest hundredth place

Calculation of the sales tax amount: $4.46

Adding the sales tax to the original price to find the total cost

Aligning decimals when adding money amounts

Final total cost calculation: $63.95

Conclusion and summary of the sales tax calculation process

Gratitude expressed to viewers for watching the tutorial

Transcripts

[Music]

welcome to math with mr j

[Music]

in this video i'm going to cover how to

calculate sales tax by hand so we're

going to write everything out without

using a calculator this will show all of

the steps for calculating sales tax and

then the total cost with the sales tax

included let's jump into our example

where we have 59.49

plus a sales tax rate of 7.5 percent so

the first thing that we need to do is to

calculate how much sales tax we will be

paying we do this by multiplying the

price by the tax rate now the tax rate

is in the form of a percent so we want

to get this percent to decimal form

percent means per 100 so we divide the

percent by 100 to convert it to a

decimal we can do this by moving the

decimal twice to the left and it's as

simple as that so let's move our decimal

twice to the left to change this to

decimal form

so i'm going to rewrite it underneath

here that way i have enough room so we

have 7.5

sales tax let's divide that by 100 which

we can do by moving the decimal once

and then twice to the left that changes

our percent to a decimal we fill the

tenths place with a zero and i'm going

to put a zero in the ones place as well

to show that we do not have any whole

numbers here so our decimal form of 7.5

percent is 0.075

once we have that we can multiply our

price by that decimal and that's going

to give us 7.5 percent of 59.49 so let's

multiply our original price by the tax

rate in decimal form so we have 59

49

times

0.075

and i'm going to go to the right in

order to solve this so when we multiply

decimals we can take the decimals out

and then place the decimal in our answer

at the end so let's do

5

9

4

9

times

75 and again we will worry about the

decimal at the end so five times nine

forty-five

five times four is twenty plus four is

twenty-four

five times nine is 45 plus 2 is 47

and then 5 times 5 is 25 plus 4

is 29 so we are done with this 5 the 4

the 2 and the 4.

we need our 0 here because we are moving

1 place value to the left and we start

with 7 times 9 which is

63 so carry our 6

seven times four is twenty-eight plus

six

thirty-four

seven times nine is sixty-three plus

three is sixty-six

and then 7 times 5 is 35 plus 6 is 41.

so now we add

5 plus 0 is 5

4 plus 3

is seven

seven plus four

is eleven

one plus nine is ten plus six

is sixteen

one plus two is three plus one is four

and then we have a 4

over here

so now we place our decimal so we look

back at the original problem and see how

many digits are to the right of a

decimal or behind the decimal so we have

one

two

three

four

five

five digits are to the right of a

decimal within our original problem that

means our answer needs five digits to

the right of the decimal so we can count

off one

two

three

four

five our decimal is placed in between

the fours let me rewrite our final

answer here without those lines

underneath

now we are working with money so

whenever we are working with money our

final answer is going to go to the

hundredths place

so we need to round this decimal to the

hundredths place

we have a six in the hundredths

we look at the digit to the right we

have a one so that means we stay the

same our answer

is going to be four dollars

and 46 cents

so that's how much we are paying in

sales tax that's 7.5

of 59.49

cents once we have that information we

take the original price and add that

sales tax that's going to give us our

final price the total cost

so we need to do our price of

59.49

and then add

our sales tax of four dollars

and 46 cents

and that will give us our final price

the total cost so let's go to the right

and add these now when adding decimals

we need to line up our decimals so we

have

59

49

and then 4

46

so lining up those decimals will line up

all of our places so let's add the

hundredths first nine plus six

fifteen

one plus four is five plus four is nine

bring our decimal straight down it's

lined up throughout the entire problem

nine plus four is thirteen

and then one plus five gives us six

so we get

sixty three dollars and ninety five

cents for our total cost that final

price with sales tax included so let's

write that over here so 63 dollars

and 95 cents

for our total cost there

so there you have it there's how you

calculate sales tax by hand

i hope that helped

thanks so much for watching

until next time

peace

you